What are the six trig function values of 5pi?

1 Answer
sente
Dec 31, 2015

sin(5pi) = 0
cos(5pi) = -1
tan(5pi) = 0
sec(5pi) = -1
csc(5pi) is "undefined"
cot(5pi) is "undefined"

Explanation:

First, let's note that sine and cosine are periodic with period 2pi, meaning for any integer k,
sin(x) = sin(x+k2pi) and cos(x) = cos(x+k2pi)
With this, we get the first two desired values:

sin(5pi) = sin(pi + 2(2pi)) = sin(pi) = 0
and
cos(5pi) = cos(pi+2(2pi)) = cos(pi) = -1

The remaining trig functions are just functions of sine and cosine.

tan(5pi) = sin(5pi)/cos(5pi) = 0/(-1) = 0

sec(5pi) = 1/cos(5pi) = 1/(-1) = -1

csc(5pi) = 1/sin(5pi) = 1/0 is "undefined"

cot(5pi) = cos(5pi)/sin(5pi) = (-1)/0 is "undefined"

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